Interference cancellation stands as an important component of contemporary and developing communication systems. For example, interference cancellation performance affects transmission power requirements and link utilization efficiencies in both the uplinks and downlinks of wireless communication systems, such as cellular communication networks based on the Wideband Code Division Multiple Access (WCDMA) or IS-2000 standards. Put simply, better interference cancellation enables data transmission at lower power levels and/or at higher data rates than would otherwise be possible.
As might be expected, the particulars of interference cancellation vary as a function of many variables, such as the communication signal types and protocols involved, details of the transmitting and receiving equipment, etc. However, providing good interference cancellation performance not infrequently requires significant signal processing resources, owing to the need for characterizing and suppressing received signal interference in real time.
For example, G-Rake receivers use extra despreading fingers to improve demodulation. To determine the finger delays, a probing approach may be used, in which weights are computed for a candidate set of delays and then re-computed for a selected set of finger delays. In general, candidate delays and finger delays are referred to as processing delays. Similarly, chip equalizers use processing delays corresponding to equalizer tap locations.
Impairment cross-correlations can be represented as an impairment covariance matrix Ru, and that matrix in turn can be used to generate the combining weights used by the G-Rake receiver in combining despread data values. By computing the combining weight vector, w, as,w=Ru−1h  Eq. (1)the G-Rake receiver uses the impairment covariance matrix to whiten colored interference in the received signal(s) of interest, where h is the net channel response vector.
There are several approaches for generating Ru in the G-Rake context, depending on the involved variant of G-Rake receiver. For example, “parametric” G-Rake receivers consider the impairments covariance matrix as a sum or combination of different interference contributions, including contributions from own-cell interference, white noise, and other-cell interference. With this parametric model, and assuming the reception of signals from J+1 network base stations, the impairment covariance matrix is given by
                              R          u                =                                                            E                c                            ⁢                              R                I                                      +                                          N                0                            ⁢                              R                n                                      +                                          ∑                                  j                  =                  1                                J                            ⁢                                                          ⁢                                                E                  c                  j                                ⁢                                  R                  O                  j                                                              =                                                    N                0                            ⁢                              R                n                                      +                                          ∑                                  j                  =                  0                                J                            ⁢                                                          ⁢                                                E                  c                  j                                ⁢                                  R                  O                  j                                                      -                          hh              H                                                          Eq        .                                  ⁢                  (          2          )                    where Ec=average energy transmitted per chip of own-cell base station, N0=one-sided power spectral density of white noise, Ecj=average energy transmitted per chip of jth other-cell base station, RI=own-cell interference covariance matrix, Rn=white noise passed through pulse shaping filter covariance matrix, and ROj=jth other-cell interference covariance matrix. (Note that the second formulation of Eq. (2) emphasizes that the own-cell interference term can be computed in a fashion similar to that used for other-cell interference, provided that a benign signal term is subtracted—e.g., RI=RO0−hhH. Assuming that other-cell interference is not modeled as white noise, the computation of RI contributes significantly to the overall complexity of a parametric G-Rake receiver operation.
One mechanism for calculating entries for RI is given by,
                                          R            I                    ⁡                      (                                          d                1                            ,                              d                2                                      )                          =                              ∑                          l              =              0                                      L              -              1                                ⁢                                          ⁢                                    ∑                              q                =                0                                            L                -                1                                      ⁢                                                  ⁢                                          g                l                            ⁢                              g                q                *                            ⁢                                                ∑                                                            m                      =                                              -                        ∞                                                              ,                                          m                      ≠                      0                                                                            m                    =                    ∞                                                  ⁢                                                                  ⁢                                                                            R                      p                                        ⁡                                          (                                                                        d                          1                                                -                                                  mT                          c                                                -                                                  τ                          l                                                                    )                                                        ⁢                                                            R                      p                      *                                        ⁡                                          (                                                                        d                          2                                                -                                                  mT                          c                                                -                                                  τ                          q                                                                    )                                                                                                                              Eq        .                                  ⁢                  (          3          )                    where gl represents the lth medium coefficient, dk is the kth finger delay, τj is the jth channel delay, Tc is a CDMA chip period, and Rp(*) is the autocorrelation of the receive pulse shaping filter. (Note that if the transmit and receive pulse filters are not the same, then Rp(*) includes convolution of the transmit and receive pulse filters.)
By manipulation, Eq. (3) is shown to be equivalent to
                                                        R              I                        ⁡                          (                                                d                  1                                ,                                  d                  2                                            )                                =                                    ∑                              l                =                0                                            L                -                1                                      ⁢                                                  ⁢                                          ∑                                  q                  =                  0                                                  L                  -                  1                                            ⁢                                                          ⁢                                                g                  l                                ⁢                                                      g                    q                    *                                    ⁡                                      [                                                                                            R                          pp                                                ⁡                                                  (                                                                                    Δ                              1                                                        -                                                          Δ                              2                                                                                )                                                                    -                                                                                                    R                            p                                                    ⁡                                                      (                                                          Δ                              1                                                        )                                                                          ⁢                                                                              R                            p                            *                                                    ⁡                                                      (                                                          Δ                              2                                                        )                                                                                                                ]                                                                                      ⁢                                  ⁢        where        ⁢                                  ⁢                                            Δ              1                        =                                                            d                  1                                -                                                      τ                    l                                    ⁢                                                                          ⁢                  and                  ⁢                                                                          ⁢                                      Δ                    2                                                              =                                                d                  2                                -                                  τ                  q                                                              ,                                          ⁢                                    and              ⁢                                                          ⁢                                                R                  pp                                ⁡                                  (                                                            Δ                      1                                        -                                          Δ                      2                                                        )                                                      =                                          ∑                                  m                  =                                      -                    ∞                                                  ∞                            ⁢                                                          ⁢                                                                    R                    p                                    ⁡                                      (                                                                  Δ                        1                                            -                                              mT                        c                                                              )                                                  ⁢                                                                            R                      p                      *                                        ⁡                                          (                                                                        Δ                          2                                                -                                                  mT                          c                                                                    )                                                        .                                                                                        Eq        .                                  ⁢                  (          4          )                    Rpp(*) can be pre-computed, thereby saving run-time computations, such that the signal processing implementation of Eq. (4) reduces to a few table lookups and a multiplication. However, the table lookup for Rpp(*) is somewhat complicated because it depends not only on the difference between Δ1 and Δ2, but also at what sample phase the difference occurs. Also, because Rpp(*) is not symmetric, one must also account for positive and negative delay differences in selecting lookup table entries.
Because of the above complications, the required table lookup operations depend on a greater number of variables, meaning more processing decisions have to be made to identify proper table entries, which in turn requires greater processing power or speed and a greater amount of working memory. Such complications detract from the efficiency gains otherwise afforded by the implementation of Eq. (4) for RI computation in a parametric G-Rake receiver.
Another approach expresses RI as,
                                                                                          R                  I                                ⁡                                  (                                                            d                      1                                        ,                                          d                      2                                                        )                                            =                                                                    ∑                                          l                      =                      0                                                              L                      -                      1                                                        ⁢                                                                          ⁢                                                            ∑                                              q                        =                        0                                                                    L                        -                        1                                                              ⁢                                                                                  ⁢                                                                  g                        l                                            ⁢                                                                        g                          q                          *                                                [                                                                              R                            ⁡                                                          (                                                                                                n                                  1                                                                ,                                                                  n                                  2                                                                                            )                                                                                -                                                                                    1                                                              N                                2                                                                                      ⁢                                                                                          ∑                                                                  m                                  =                                                                      1                                    -                                    N                                                                                                                                    N                                  -                                  1                                                                                            ⁢                                                                                                                          ⁢                                                                                                (                                                                      N                                    -                                                                                                                                     ⁢                                                                                                                                                                      ⁢                                                                                                    m                                                                                                                                                                                                      )                                            ⁢                                                                        R                          p                                                (                                                                              d                            1                                                    -                                                                                             ⁢                                              mT                        c                                                                                            -                                  τ                  l                                                      )                    ⁢                                    R              p              *                        ⁡                          (                                                d                  2                                -                                  mT                  c                                -                                  τ                  q                                            )                                      ]                            Eq        .                                  ⁢                  (          5          )                    From inspection, Eq. (5) has similarities to the formulation given in Eq. (4) but with R(n1,n2) equivalent to (and replacing) Rpp(*), and a more complicated expression involving the sum of products of Rp(*). Under limited reception conditions—i.e., minimal time dispersion in the propagation channel—the lookup tables for R(n1,n2) and Rp(*) need only span a few CDMA spreading chips to yield acceptable performance. However, Eq. (5) does not necessarily yield good performance over a range of channel conditions, and still entails significant computational complexity.